Finite element transport modeling using analytic element flow solutions
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Bibliographic record
Abstract
Finite element methods for solute transport simulation typically use a discrete representation of the flow domain obtained from a finite element solution of the associated groundwater flow problem. Velocity, saturated thickness, and components of the dispersion coefficient tensor are represented as a set of nodal and/or element‐averaged values. In contrast, the analytic element method (AEM) provides continuous mesh‐independent solutions for these variables. In this paper, a set of techniques for using two‐dimensional AEM flow solutions as the basis of finite element solute transport models is introduced. First, a general AEM‐based discretization approach is presented that addresses the existence of curved boundaries, singularities, and discontinuities in vertically averaged concentration. Second, residual integration methods that handle continuous parameters with internal and boundary singularities are developed and evaluated. Third, an approach is introduced for handling internal discontinuities in concentration across certain analytic elements. This new approach uses a nonstandard mesh topology and a new formulation for internal coupled boundary conditions. The AEM‐based transport simulation methods introduced in this paper are demonstrated to be robust and accurate for a variety of test problems.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it